Abstract
As the superconducting transition temperature Tc is approached from above, Cooper pair fluctuations grow in amplitude, and the pair susceptibility (which measures the tendency of pairs to form in response to an external “pair field”) diverges. This article studies this divergence in mean field theory. An elementary derivation of the BCS equation for Tc is constructed in exact analogy with the Curie-Weiss mean field theory of ferromagnetism. The possibility of “antisuperconductivity” (in analogy with antiferromagnetism is discussed. The coherence length ξo governing the spatial range of fluctuations is derived. These results are then generalized to include strong-coupling effects and both non-magnetic and paramagnetic impurities. The results of Abrikosov and Gorkov for the depression of Tc by paramagnetic impurities and the depression of ξo by non-magnetic impurities are derived including strong-coupling mass-renormalization corrections. All results are expressed in a form valid for arbitrarily complicated electronic band structure.
Keywords
- Coherence Length
- Superconducting Transition Temperature
- Magnetic Impurity
- Landau Theory
- Linear Response Theory
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Supported in part by U.S. National Science Foundation Grant no. DMR79-00837.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
J. Bardeen, L.N. Cooper, and J.R. Schrieffer, Phys. Rev. 108, 1175 (1957).
G.M. Eliashberg, Zh. Eksp. Teor. Fiz. 38, 966 (1960); 39, 1437 (1960). [Sov. Phys. JETP 11, 696 (1960); 12, 1000 (1961)].
D.J. Scalapino, in Superconductivity, edited by R.D. Parks (Marcel Dekker, New York, 1969).
P. Nozieres, Theory of Interacting Fermi Systems, W.A. Benjamin, New York, 1961, Ch. 2.
S. Doniach and E.H. Sondheimer, Green’s Functions for Solid State Physicists, W.A. Benjamin, Reading, Mass., 1974; Sec. 5.5 and Appendix 2.
D.J. Thouless, Ann. Phys. (NY) 10, 553 (1960).
C. Kittel, Quantum Theory of Solids, J. Wiley and Sons, New York, 1963; p. 151.
V.L. Ginzburg, Fiz. Tverd. Tela 2, 2031 (1960) [Sov. Phys. Sol. State 2, 1824 (1960)].
B.L. Gyorffy, in Superconductivity in d-and f-Band Metals, (D.H. Douglass, ed.), Plenum, New York, 1976, p. 29; I.F. Foulkes and B.L. Gyorffy, Phys. Rev. B15, 1395 (1977).
G. Bergmann and D. Rainer, Z. Phys. 263, 445 (1973).
P.B. Allen and R.C. Dynes, Phys. Rev. B12, 905 (1975).
W.L. McMillan, Phys. Rev. 167, 331 (1968).
A.A. Abrikosov and L.P. Gor’kov, Zh. Eksp. Teor. Fiz. 36, 319 (1959); 39, 1781 (1960). [Sov. Phys. JETP 9, 220 (1959); 12, 1243 (1961)].
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1980 Springer-Verlag
About this paper
Cite this paper
Allen, P.B. (1980). Theory of superconducting transition temperature, pair susceptibility, and coherence length. In: Pękalski, A., Przystawa, J.A. (eds) Modern Trends in the Theory of Condensed Matter. Lecture Notes in Physics, vol 115. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120145
Download citation
DOI: https://doi.org/10.1007/BFb0120145
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-09752-5
Online ISBN: 978-3-540-38628-5
eBook Packages: Springer Book Archive